Despite the apparent success of advanced process control, the proportional-integral-derivative (PID) control still remains the main type of control in the process industries. PID controllers and their variations such as proportional-integral (PI), proportional-derivative (PD), and proportional (P) controllers are implemented as either stand-alone controllers or configurable software modules within the distributed control systems (DCS). The DCS software is constantly evolving providing a number of new features, among which the controller autotuning functionality is one of most useful.
Tuning of PID controllers based on relay feedback tests proposed by Astrom and Hagglund in 1981 (respective U.S. Pat. No. 4,549,123 issued in 1985) received a lot of attention after that (W. L. Luyben, “Derivation of Transfer Functions for Highly Nonlinear Distillation Columns”, Ind. Eng. Chem. Res. 26, 1987, pp. 2490-2495; Tore Hagglund, Karl J. Astrom, “Industrial Adaptive Controllers Based on Frequency Response Techniques”, Automatica 27, 1991, pp. 599-609). It identifies the important dynamic information, ultimate gain and ultimate frequency, in a straightforward manner. The success of this type of tuners lies on the fact that they are simple and reliable. These features of the relay feedback autotuning have lead to a number of commercial tuners (Tore Hagglund, Karl J. Astrom, “Industrial Adaptive Controllers Based on Frequency Response Techniques”, Automatica 27, 1991, pp. 599-609) and industrial applications (H. S. Papastathopoulou, W. L. Luyben, “Tuning Controllers on Distillation Columns with the Distillate-Bottoms Structure”, Ind. Eng. Chem. Res. 29, 1990, pp. 1859-1868).
Despite the apparent success of relay based tuning, it can lead to reduced or vice versa excessively large gain and phase margins because of the choice of the test point (frequency of the oscillations) corresponding to the phase lag of the process equal to −180° (phase cross-over frequency ωπ) while inclusion of the controller in the loop introduces additional phase shift, which was not accounted for at the selection of the test point and designing the tuning rules.